Parametrized braid groups of chevalley groups

Jean Louis Loday*, Michael R. Stein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We introduce the notion of a braid group parametrized by a ring, which is defined by generators and relations and based on the geometric idea of painted braids. We show that the parametrized braid group is isomorphic to the semi-direct product of the Steinberg group (of the ring) with the classical braid group. The technical heart of the proof is the Pure Braid Lemma, which asserts that certain elements of the parametrized braid group commute with the pure braid group. This first part treats the case of the root system A n; in the second part we prove a similar theorem for the root system Dn.

Original languageEnglish (US)
Pages (from-to)391-416
Number of pages26
JournalDocumenta Mathematica
Issue number1
StatePublished - 2005


  • Braid group
  • Parametrized braid group
  • Root system
  • Steinberg group

ASJC Scopus subject areas

  • Mathematics(all)


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